Pump requirements for betatron-generated femtosecond X-ray laser at saturation from inner-shell transitions

We study pump requirements to produce femtosecond X-ray laser pulses at saturation from inner-shell transitions in the amplified spontaneous emission regime. Since laser-based betatron radiation is considered as the pumping source, we first study the impact of the driving laser power on its intensity. Then we investigate the amplification behavior of the K-α transition of nitrogen at 3.2 nm (395 eV) from radiative transfer calculations coupled with kinetics modeling of the ion population densities. We show that the saturation regime may be experimentally achieved by using PW-class laser-accelerated electron bunches. Finally, we show that this X-ray laser scheme can be extended to heavier atoms and we calculate pump requirements to reach saturation at 1.5 nm (849 eV) from the K-α transition of neon.